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# Fluid Flows Around Complex 3D Objects

Figure 1. Flow around a submarine:
Finite element mesh.

Numerical simulations are able to analyse and predict real physical processes through the use of special mathematical and computational techniques. Such simulations take place on powerful supercomputers, often employing parallel processing. These highly specialized methods require detailed expertise in three core disciplines: engineering, mathematics and computer science.

Through numerical computer simulation we are able to understand and control the performance of complex mechanisms and systems before their production is undertaken. For example, in naval engineering, a computer simulation of a submarine hull can substitute for the time-intensive and costly experiments in the water tunnel.

As a result, numerical simulation has gained significant importance in various key areas of the global economy: most recently in the biomedical and bioengineering area, but clearly also in automobile, aeronautical and aerospace industry, as well as electrical and chemical industry. With the declining need to do research through experiments, money, time and valuable resources can be saved, and novel types of analyses can be performed.

Figure 2. Flow around a submarine:
Pressure distribution.

Within the field of numerical simulation, our research focus is on the modeling of fluids—especially, the ability to model both, steady and time-dependent, fluid flows around complex three-dimensional objects. For this purpose, over the last 10 years, we have developed a computer code (i.e., fluid flow solver) based on the Finite Element Method, and relying on the velocity-pressure formulation of the incompressible Navier-Stokes equations. The variational form of these equations is stabilized by using consistent Galerking/Least-Squares techniques in order to provide robust and accurate solutions at all flow conditions. Turbulence models of Smagorinsky and Spalart-Allmaras are used for computations involving high Reynolds numbers.

This scalable flow solver operates on a range of parallel computers, including IBM Blue Gene, Sun Fire and PC clusters. As an example application shown here, the flow solver has been used to compute water flow around a Los Angeles-class submarine with a spinning propeller at Reynolds number 1×109. Figure 1 shows the surface of the unstructured volume mesh, which consists of 808,987 tetrahedral elements. Figure 2 shows the pressure contours on the submarine hull.

While numerical simulation is steadily evolving into a major research tool, certain application areas still prove to be particularly challenging. These areas form our major research interests.

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